Complexly fractionated syllogistic quantifiers

Journal of Philosophical Logic 20 (3):287 - 313 (1991)
Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantificrs, and then include further quantifiers which are modifications of such fractions (such as "almost ½ the S are P" and "Much more than ½ the S are P"). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes & Peterson (forthcoming) for proofs of the unsoundness and incompleteness of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., "almost ¾ the S arc P'" is represented as " -(3(SP) » SP)"
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DOI 10.1007/BF00250542
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References found in this work BETA
Philip L. Peterson (1979). On the Logic of ``Few'', ``Many'', and ``Most''. Notre Dame Journal of Formal Logic 20 (1):155-179.
Philip L. Peterson (1985). Higher Quantity Syllogisms. Notre Dame Journal of Formal Logic 26 (4):348-360.
Bruce E. R. Thompson (1986). Syllogisms with Statistical Quantifiers. Notre Dame Journal of Formal Logic 27 (1):93-103.

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Citations of this work BETA
Fred Johnson (1994). Syllogisms with Fractional Quantifiers. Journal of Philosophical Logic 23 (4):401 - 422.
Philip L. Peterson (1995). Distribution and Proportion. Journal of Philosophical Logic 24 (2):193 - 225.

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